Associative property in fraction multiplication

Perhaps best, prior to addressing an explanation of associative property, present in fraction multiplication, is to briefly revise some definitions, which will allow us to understand this Mathematical Law within its precise context.


Fundamental definitions

In this sense, it may also be best to delimit this theoretical review to two specific notions: first, it will be erected as prudent to begin with the very definition of Fractions, as this will be crucial to take into bear in mind the nature of the mathematical expressions on the basis of which the operation is given, which gives rise to the associative mathematical property.

Likewise, it will be necessary to be aware of the concept of Fraction Multiplication, because it is the operation where this property takes place. Here are each of these concepts:

Fractions

Therefore, it can be said that Mathematics has generally defined Fractions as a type of expression with which it is aware of fractional numbers, so that then one of the ways in which the amounts are represented inaccurate or unaware.

Likewise, this discipline has indicated that fractions will consist of two elements, each of which has been described as follows:

Numerator: In this way, the numerator will be distinguished, which will constitute the number or value intended to occupy the top of the fraction, while indicating how many parts of the whole represents the fraction.

Denominator: on the other hand, the second element of the fraction will be the denominator, which is located at the bottom of the expression, indicating in how many parts the whole of which a part is taken is divided.

Multiplication of fractions

In another order of ideas, it will also be relevant to throw lights on the definition of Fraction Multiplication, then understanding that this can be explained as a mathematical operation in which you seek to determine what the result is that is obtained once you are has added a fraction on its own, so many times as a second fraction points out, hence this mathematical procedure is defined by some authors as a type of abbreviated sum.

With regard to the correct way in which this operation should be resolved, most authors indicate that a product should be obtained among the numbers that constitute the numerators of the fractions, while the elements that work will be carried out equally denominators, operations that can be mathematically expressed as follows:

Associative property of fraction multiplication

Once these concepts have been brought to the chapter, it may certainly be much easier to approach the definition of associative Property that takes place in the Multiplication of fractions, and which has been understood as the Mathematical Law that dictates than in all operation of this type, the different fractions that serve as elements or factors can establish different associations between them, without this meaning an alteration of the final product, which can be expressed mathematically as follows:

Example of Associative Property in Fraction multiplication

However, the most efficient way to complete an explanation of associative property, present in fraction multiplication, may be through the exposure of a particular example, which allows us to see in practice how actually in an operation of multiplication in which three or more fractions are involved, the different relationships or associations established by these expressions are indifferent, for the same result will always be obtained, as can be seen below:

Check the Associative Property in Fraction Multiplication:

First Association:

Second association:

Therefore:

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Associative property in fraction multiplication
Source: Education  
September 26, 2019


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